Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

Elemental distribution by synchrotron X-ray microfluorescence of prostate 3D cell culture

Prostate cancer is a highly prevalent disease and ranks second among malignant neoplasms that affect men around the world, behind lung cancer alone. Trace elements are very important and are involved in many cellular processes. The X-ray microfluorescence technique is an advanced tool of high spatial resolution, sensitivity, multielemental analysis, and nondestructiveness for trace element study. This study aimed to investigate the elemental distribution in spheroids obtained through the following human prostate cell lines using synchrotron X-ray microfluorescence: tumor cell line androgen independent (DU145), tumor cell line androgen dependent (LNCaP), and normal cell line (RWPE-1). The measurements were performed with a standard geometry of 45° of incidence, excited by a white beam using a pixel of 25 μm and an acquisition time of 300 ms/pixel at the X-ray fluorescence beamline at the Synchrotron Light National Laboratory (Campinas, Brazil). The synchrotron X-ray microfluorescence results showed differences between groups in all elements analyzed and suggested that further studies should be performed to understand the relationship of these trace elements with the progression and development of the disease.     

Wimp searches with gamma rays in the Fermi era: Challenges,methods and results

The launch of the gamma-ray telescope Fermi Large Area Telescope (Fermi-LAT) started a pivotal period in indirect detection of dark matter. By outperforming expectations, for the first time a robust and stringent test of the paradigm of weakly interacting massive particles (WIMPs) is within reach. In this paper, we discuss astrophysical targets for WIMP detection and the challenges they present, review the analysis tools which have been employed to tackle these challenges, and summarize the status of constraints on and the claimed detections in the WIMP parameter space. Methods and results will be discussed in comparison to Imaging Air Cherenkov Telescopes. We also provide an outlook on short term and longer term developments.